Leicestershire Police said the three-month pilot was launched earlier this year to see whether only responding to half of attempted burglaries had any impact on victim satisfaction rates.

For the purposes of the pilot, attempted burglaries at even-numbered houses would be fully investigated with forensic teams sent and fingerprints taken but this would not happen if the victim lived in an odd-numbered house.

The force added that if the victim was deemed vulnerable or the suspected burglary was part of a series of crimes, the property would be visited by officers regardless of house number.

Leicestershire Police said the pilot saw police officers attending all scenes of attempted burglary, but only sending forensic teams to half of all potential crime scenes had "no noticeable impact on victim satisfaction".

Jo Ashworth, director of forensic sciences, at the East Midlands special operations unit, said: "The pilot was developed to look at what value forensic teams bring to the detection of attempt burglaries. At a time when we are operating within reduced budgets, it is even more critical that we make the absolute best use of our crime scene investigators' time."

Leicestershire's deputy chief constable Roger Bannister said: "The public would expect us to make the very best possible use of our time and limited resources to have the biggest impact on public safety and the prevention and detection of crime.

"This pilot suggests that we may need to reconsider how best to deploy crime scene investigators, especially if we are currently sending them automatically to scenes where, despite their professionalism and expertise, there is no evidence for them to retrieve."

Sir Clive Loader, Leicestershire's police and crime commissioner, said he did not know about the scheme and would have advised against it taking place.

He added: "I ap preciate that technically this is operational policing territory, carried out by an East Midlands collaborative unit, I believe that I should have been informed, principally because it was taking place in Leicestershire.

"Had I been consulted I would have advised against it, particularly in light of the controls chosen which, to me at least, are unlikely to inspire much public confidence."

The pilot scheme was tested after analysis showed that forensic officers were sent to 1,172 attempted burglaries in the region but few scenes were found to contain any scientific evidence. Only 33 suspects were identified as a result of these visits, police said.

Jonathan Ashworth, Labour MP for Leicester South, said his constituents would be "outraged" by the policy.

He said: "It's a daft and crazy scheme. Why should people who live in odd numbered houses get a lesser service from their local police force? They pay their taxes to fund them too."

He added he would be writing to Theresa May to find out if ministers knew about the pilot scheme.

The Home Office spokesperson said they were not made aware of the pilot scheme - but added it did not need to be as operational decisions were made by individual forces.

A spokeswoman added: "We are clear that all reported crimes should be taken seriously, investigated thoroughly and, where appropriate, taken through the courts and met with tough sentences.

"Since 2010, the Government has brought in a number of reforms that have made it easier for the police to do their job by cutting red tape, scrapping unnecessary targets, and giving forces the discretion to use their professional judgment."